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1 results

  • Holomorphic Functions of Exponential Growth on Abelian Coverings of a Projective Manifold

  • Alexander Brudnyi
  • Journal:
    Compositio Mathematica / Volume 127 / Issue 1 / May 2001
    Published online by Cambridge University Press:
    04 December 2007, pp. 69-81
    Print publication:
    May 2001
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  • Let M be a projective manifold, p: MG→M a regular covering over M with a free Abelian transformation group G. We describe the holomorphic functions on MG of an exponential growth with respect to the distance defined by a metric pulled back from M. As a corollary, we obtain Cartwright and Liouville-type theorems for such functions. Our approach brings together the L2 cohomology technique for holomorphic vector bundles on complete Kähler manifolds and the geometric properties of projective manifolds.